Problem: What do the following two equations represent? $4x+4y = -2$ $-20x-20y = -1$
Solution: Putting the first equation in $y = mx + b$ form gives: $4x+4y = -2$ $4y = -4x-2$ $y = -1x - \dfrac{1}{2}$ Putting the second equation in $y = mx + b$ form gives: $-20x-20y = -1$ $-20y = 20x-1$ $y = -1x + \dfrac{1}{20}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.